Question: Solve for $x$ and $y$ using elimination. ${-2x-5y = -61}$ ${3x+3y = 51}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${-6x-15y = -183}$ $6x+6y = 102$ Add the top and bottom equations together. $-9y = -81$ $\dfrac{-9y}{{-9}} = \dfrac{-81}{{-9}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-2x-5y = -61}\thinspace$ to find $x$ ${-2x - 5}{(9)}{= -61}$ $-2x-45 = -61$ $-2x-45{+45} = -61{+45}$ $-2x = -16$ $\dfrac{-2x}{{-2}} = \dfrac{-16}{{-2}}$ ${x = 8}$ You can also plug ${y = 9}$ into $\thinspace {3x+3y = 51}\thinspace$ and get the same answer for $x$ : ${3x + 3}{(9)}{= 51}$ ${x = 8}$